WASHINGTON — President Barack Obama will release a budget next week that proposes significant cuts to Medicare and Social Security and also embraces tax increases, an approach that he hopes will persuade Republicans to sign on to a fiscal grand bargain.

The document will incorporate the compromise offer Obama made to House Speaker John Boehner, R-Ohio, in December in the discussions over the “fiscal cliff” — which included $1.8 trillion in deficit reduction through spending cuts and tax increases.

“It’s not our ideal policy. It’s a compromise that we’re willing to do to get a bigger deal,” said a senior White House official. “We want to make clear that it’s something that we’re willing to do. To not put it in [the budget] would be a conversation disconnected with reality.”

The senior official added that including the offer was not a hard call. Failing to do so, the official said, would have provoked howls from Republicans that “you moved the goal posts.”

Boehner, in a statement Friday, accused Obama of holding entitlement cuts “hostage” in an effort to win support for more tax-rate increases, despite warnings from congressional Republicans not to do so.

“That’s no way to lead and move the country forward,” Boehner said.

He also criticized the budget proposal because it does not balance, although according to White House estimates it would significantly reduce the deficit as a percentage of the economy over the next decade.

The president also is likely to face immediate heat from some Democrats and liberal supporters over his proposed cuts to entitlement programs.

Obama proposes, for instance, to change the cost-of-living calculation for Social Security in a way that will reduce benefits for most beneficiaries, a key Republican request that he had earlier embraced only as part of a compromise. Many Democrats say they are opposed to any Social Security cuts and are likely to be furious that such cuts are being proposed as official administration policy.

The full budget will be released Wednesday, but officials gave a top-line overview to reporters Friday and have previously released details of the offer to Boehner.

Obama’s budget, for the fiscal year starting Oct. 1, would fund several new priorities, including the creation of a new program offering preschool to all 4-year-olds from low- and moderate-income backgrounds and a significant new investment in brain research.

Officials propose an increase in tobacco taxes to pay for the early childhood education initiative and would also seek to generate revenue by limiting how much wealthy individuals can accrue in their tax-retirement accounts. Such accounts would be capped at $3 million in 2013 dollars — which officials say is enough to finance a $205,000 a year income. He would also seek to scrap a loophole in the law that lets people collect both unemployment insurance and disability payments — so called “double-dipping.”

The budget request comes on top of a deal struck at the start of the year to raise taxes on the wealthy by more than $600 billion over a decade — mainly by returning to Clinton-era rates for households earning over $450,000 annually.

Through that pact and earlier agreements, Congress and Obama have agreed to reduce the annual budget deficit — how much more the government spends than it collects — by $2.5 trillion over the next decade.

If left in place, the deep spending cuts that took effect March 1, known as sequestration, would reduce the deficit by an additional $1.2 trillion over the same period. That would be just about enough to keep deficits from rising and to stabilize the debt, as measured as a percentage of the overall economy.

Obama’s budget proposal, however, would eliminate sequestration and replace it with other deficit reduction measures, together worth $1.8 trillion, according to White House estimates. The deficit, which is projected this year to be equal to 5.5 percent of the size of the economy, would shrink to 1.7 percent of the economy by 2023.

The budget is more conservative than Obama’s earlier proposals. Obama is seeking to raise $580 billion in tax revenue by limiting deductions for the wealthy and closing loopholes for certain industries like oil and gas. Those changes are in addition to the increased tobacco taxes and more limited retirement accounts for the wealthy that are meant to pay for new spending.

The budget proposal slices $200 billion from already tight defense and domestic budgets. It would cut $400 billion from Medicare and other health programs by negotiating better prescription drug prices and asking wealthy seniors to pay more, among other policies.

It would also generate $200 billion in savings by scaling back farm subsidies and federal retiree programs, among other proposals.

The proposal to change the formula to calculate Social Security payments, also originally part of the offer to Boehner, would generate $130 billion in savings and $100 billion in revenue, a result of the impact of the formula change on other government programs.

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